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    • ▾Bridge course
      • •Countable and uncountable sets
      • ▸Proof techniques
        • •Example of a nonconstructive proof
        • •Direct proof
        • •Disproof by counterexample
        • •Proof by cases
        • •Proving properties of absolute value
        • •Proof by contrapositive
        • •Proof by contradiction
        • •Proof by induction
        • •Proof by strong induction
        • •Proving de Moivre's theorem
        • •Visual proof
        • •Challenge
      • ▸Relations
        • •Equivalence relations
        • •Intersection of equivalence relations
        • •Representing relations using matrices
        • ▸Combining relations
          • •Composition of relations
        • •Inverse of composite relation
        • •Representing relations using digraphs
        • •Properties of relations
        • •Proving equivalence relations
        • •What is a relation?
        • •Finding the inverse of a relation on a finite set
      • ▾Functions (bridge course)
        • ▾Injective, surjective, and bijective
          • •Intro
          • •Is it bijective? (infinite domain)
          • •Is it injective?
          • ▸Is it surjective?
            • •Proof: Composite of surjections is surjection
          • •Proving properties of injective, surjective, and bijective functions
     › Bridge course › Functions (bridge course) › Injective, surjective, and bijective

    Proving properties of injective, surjective, and bijective functions

    The composition of injective functions is injective.
    45458The Composition of Injective(one-to-one) Functions is Injective Proof
    The Math Sorcerer
    If \(g \circ f\) is injective, then \(f\) is injective.
    43934Proof that if g o f is Injective(one-to-one) then f is Injective(one-to-one)
    The Math Sorcerer
    If \(g \circ f\) is surjective, then \(g\) is surjective.
    46200Proof that if g o f is Surjective(Onto) then g is Surjective(Onto)
    The Math Sorcerer
    45594The Composition of Surjective(Onto) Functions is Surjective Proof
    The Math Sorcerer
    7927Surjection if Composite is Surjection
    ProofWiki

    YouTube videos

    • 45458The Composition of Injective(one-to-one) Functions is Injective Proof
      The Math Sorcerer